Us E Submarine Base, Groton, Conn. REPORT NUMBER DECOMPRESSION PATTERNS DEVELOPED BY AN INTERDEPENDENT ELECTRIC ANALOG by Gary P. Todd Lieutenant, MC, U. S. Naval Reserve Bureau of Medicine and Surgery, Navy Department In-House Laboratory Research Work Unit MR.-9. Approved and Released by: J. E. Stark, CAPT MC USN COMMANDING OFFICER Naval Submarine Medical Center A May 99 This document has been approved for public release and sale; its distribution is unlimited.
DECOMPRESSION PATTERNS DEVELOPED BY AN INTERDEPENDENT ELECTRIC ANALOG by Gary P. Todd Lieutenant, MC, U. S. Naval Reserve SUBMARINE MEDICAL RESEARCH LABORATORY U. S. NAVAL SUBMARINE MEDICAL CENTER REPORT No. Bureau of Medicine and Surgery, Navy Department In-House Laboratory Research Work Unit MR.-9. Reviewed and Approved by: Reviewed and Approved by: ý<ý ; Charles F. Gell, M.D., D.Sc (Med) Scientific Director SubMedResLab Joseph D. Bloom, CDR MC USN Director SubMedResLab Approved and Released by: E. Stark, CAPT MC USN COMMANDING OFFICER Naval Submarine Medical Center This document has been approved for public release and sale; its distribution is unlimited.
SUMMARY PAGE THE PROBLEM To design and manufacture a simple, inexpensive electronic decompression analog. FINDINGS A simple electronic decompression analog was developed. The mathematical model of this analog differs somewhat from the Standard U. S. Navy modified Haldane model. In this analog the theoretical tissues of increasing effective half times are arranged in series as opposed to the Haldane model in which the tissues are in parallel. The application of simulated dives to this analog have resulted in decompression schedules which show interesting variation from Standard U. S. Navy Tables. APPLICATION Although the application of analog methods to decompression schedule requirements is not new, this model possesses some interesting areas to pursue where the currently used model has appeared to be inadequate. The simplicity of this analog further provides a simple and rapid method to observe the application of further modifications to this or the Haldane mathematical models. If this model proves successful on careful schedule testing, the analog could readily be used as a decompression meter in real or accelerated time. ADMINISTRATIVE INFORMATION This investigation was conducted as a part of In-House Independent Laboratory Research and Work Unit MR.-9. The present report was approved for publication on May 99 and has been designated as Submarine Medical Center, Submarine Medical Research Laboratory Report No.. This is the final report on the work unit listed above. PUBLISHED BY THE NAVAL SUBMARINE MEDICAL CENTER ii
ABSTRACT A simple, inexpensive electronic analog has been developed and constructed which is based on a modification to the classical Haldane mathematical model. Unlike the Haldane model this analog uses a series alignment of theoretical half-time tissues rather than the usual parallel arrangement. Schedules produced by this analog closely follow the experimental inert gas elimination curves developed by Behnke and the mathematical model theorized by B. A. Hills. The results raise an interesting question as to the adequacy of the present Haldane model modification employed by the U. S. Navy for decompression schedule calculation. Further studies must be made before this latter question can be answered. i i
DECOMPRESSION PATTERNS DEVELOPED BY AN INTERDEPENDENT ELECTRIC ANALOG INTRODUCTION It is known that the classical Haldane model for calculating decompression tables had weaknesses in that it deviated from empirical data in short shallow dives and in prolonged or deep dives. In general, his model gave too long a decompression for shallow dives and too short in prolonged or deep dives. In practice, these weaknesses have been largely overcome by empirically modifying the tissue ratios allowed at varying depths, and by adding longer half-time tissues to the model. It has also been known for some years that obese persons do poorly on long, deep dives, but that they appear to do much better than thin persons on short or shallow dives. This is usually interpreted as due to the slower fat tissues absorbing excess nitrogen from the fat tissues during decompression. This situation is not covered by the classical model. In electrical terminology, the classical model is equivalent to a bank of independent capacitor-resistor circuits, -with no spill-over between circuits (Diagram ). This study concerns the design and characteristics of a highly stable electrical model with interdependent connections (Diagram ). Using this extremely simple analog, a new series of theoretical decompression schedules has been computed. To get away from the term "tissue", which cannot be defined in this context and is therefore misleading, the term "rank" is employed to discuss the different capacitors. The analog discussed here has eight ranks; number being nearest the power supply, and number the last rank (Diagram ). DESIGN With the exception of the capacitors, and possibly the printed circuit boards, all of the parts used are readily available at modest cost (Parts List, Table I). The schematic is shown in Diagram. Symbol TABLE I. PARTS LIST R R- R 9 K 9 - o-- sw + - Item Resistor, ohm, / watt, %o Resistor, 7K ohm, / watt, % Silicon rectifier bridge, capable of handling PIV and ma mfd, vdc, electrolytic capacitors. Must be very low leakage, such as Mallory Tantalex (tantalum) Single-pole, single throw toggle switch Binding posts ( needed) Printed circuit boards, x ", not sensitized, phenolic composition () Ferric Chloride etching solution, cc Wire, ga., Teflon insulation Note: Total cost - less than $ + ~ ++ SSW- serves to isolate- external power from any of the circuitry. SRB is a silicon rectifier bridge which may be a single integrated unit or individual components. It prevents damage to the polarized capacitors in case of accidental reversal of external power leads. R-
NPUT C C 7 C9 COMMON NEGATIVE 97I., - /. ' 7 / /./~ o 7. - - - - e I - Minutes Figure -Saturation Pattern of Different Ranks of Analog. (Note how each rank appears to start saturation at different times, and how the last two ranks behave as one.)
I- 9 so 7 : -/ -7./ Eight ranks were chosen because of costthe entire budget for this project exclusive of power supply and meter being under $.. Four more ranks would double the longest half-time to about minutes in a to scale. As many as sixteen might be needed for a saturation dive. Rank TABLE II Half-Time Change in Half- Time Miutes Figure -Integrated Curve from Figure. Plus marks give data from Figure in "Behnke, A. R. and Willmon, T. L., Am. J. Physiol. :, Jan 9." Figure is a plot of measured N elimination. "-" Time Scale ::. is a relatively low resistance bleeder resistor which allows C- to discharge instantly when voltage is decreased, and also acts as a shortcircuit across the analog capacitors (C -C 9 ) for their discharge during decompression. SW- isolates the voltage reference capacitor C- from the rest of the circuit during manipulation of external voltage, if desired. Both switches remain closed ("on") during actual runs. The rest of the circuit is rather straight-forward: R -R 9 are all / watt, 7K ohm, % carbon resistors connected in series with the positive pole of the respective capacitors connected in parallel between them. Design of the circuitry with the positive pole of the capacitors between the resistors is a convenience feature, because many meters use a clip for the negative lead and a probe for the positive lead. The only critical elements in the circuit are the capacitors. The ones used were chosen because of their high capacitance, small physical size, and excellent stability. Internal leakage is about % in hours. For convenience, ten -way binding posts are used to monitor voltages at each of the analog ranks and the depth reference voltage at C-. One post is connected to the common negative ground of the analog section for the meter's negative lead. A. B. C. D. E. F. G. 7 H. 7 sec sec 9 7 9 9 9 77 97 9 7 9 9 97 7 7 7 7 9 9 7 7
Table II shows saturation half-times for eight different analogs with from to ranks, respectively. Notice the effect of a rank on neighboring ranks, and especially note the importance of the last two ranks. Figure shows the saturation pattern of each of the ranks in an eight rank analog. These data were added together to obtain an in integrated Figure. Superimposed on Figure is Behnke's empirical curve of N washout in man. Figure shows tha with saturation. Figure compared the clas- TAB %LE III Ratios of Absorbed Inelrt Gas (per analog) Upon Arriving at Various Stopis. Data from / Dive. Stop ' ' ' ' ' Below ' ' '...9.7.9...7......9.9 are "Surfacing Ra.7..7...... TABLE V Same Decompression Schedule as in Table IV, but With Only Minutes Bottom Time. / Table Used. Stop ' ' '.79...9..7... Rank.9.7..9.. Using this time scale, and presaturating rt the half-time changes the analog to atmospheric nitrogen, B. A. Hills' data on decompressing from a / dive were run through the analog (Table III). sical model to the azaalog, with time scales Because of their careful titration they are adjusted so that bot ;h rate to 9%. simultaneously satu- used as a main source of hard data for calibration of the analog. The ratios thus obtained were checked by CALIBRATION OF THE ANALOG running through the / schedule after a By actual measurement, the analog satu- minute dive and after a minute dive. rates in about sixty minutes. Setting that The former dive is considered borderline at equal to a. saturatior time of twelve hours best, while the latter is quite safe. The ratios gives a scale of secornds to the minute.... 7..7...7.9 for arriving at the different stops are given in Tables and, respectively. From these simulated dives, criteria were selected for tolerable inert pressures at each stop. These inert gas pressures are expressed as ratios of inert gas pressure to hydrostatic Rank pressure. The ratio selected for use in the 7 analog for all ranks and depths was.:..9.7... Because Hills' data shows that under..9.7.. proper conditions the diver can surface di-...9..7 rectly from deeper stops, a surfacing pres-...7.9...... sure of 7 feet of nitrogen was used in all the tios" from Hills' data: analog predicted tables. This is equivalent to r7 - - " - r, a.7: "surfacing ratio." I. U.. I.I(V. IV...7..7..7..7. Note that the simulated dive for a ' last stop was three minutes longer, and for a ' last stop was five minutes longer than Hills' actual titration times. This was done as an additional safety factor. Stop ' ' ' TABLE IV Arriving Ratios from a / Table After a -Minute Dive...7..7..... Rank.9...77.9...9. 7.7.7...7. Ascent rates were set so as not to exceed a.: ratio of absolute nitrogen pressure in the breathing mixture at diving depth to absolute hydrostatic pressure at the depth achieved at the end of a one minute ascent. One minute is chosen because it is approximately equal to normal blood circulation time. An examination of the data in Table II will reveal why it was decided to return to the original Haldane concept of using the same ratio for all depths and all tissues, except for ascent and surfacing. For, although the ratios used for constructing the original tables varied from.: down to.:, the
same dive simulated on the analog produces remarkably similar ratios for all ranks and depths. Until the decompression schedules predicted by the analog are actually tested, there can be no real advantage in juggling ratios. RESULTS Table VI gives decompression schedules from the analog using the criteria above. These are untested schedules, and are presented simply to show the pattern developed when a different model is used in calculating the schedules. The format is different in that ascent time is included in subsequent stops. No ascent time is more than one minute. For those dives which require a longer ascent, a nonstop "Stop" is given to indicate the point of ascent at the end of each minute during ascent. For example, / means to ascend to foot stop in one minute and continue without stopping to the next stop; / means to come to the surface in one minute. TABLE VI Analog Tables. Depth/Time / / / / / / 7/ 7/ 7/ / / / 9/ 9/ 9/ / / /9 / / / /9 / / /9 / / /9 / / /9 / / /9 / / /9 Total Time 7 9 9 7 9 7 9 9 9 9 7 7 9 7 9 9 9 9 9 9 7 Navy.7 9...7... 9.... 7.........7. 7.. 7....7.. 9......
These schedules are based on a hour saturation time and thus are equivalent to a maximum half-time of about minutes. This is probably adequate for the short dives included. For comparison, the United States Navy Tables of 9 are included in Table VII. Ascent time is included in the first stop. Since the analog was calibrated to Hills' titration of the / dive, it is interesting to see what the analog predicts, on that dive. Both dives are presently in Table VIII. Finally, a table of no-decompression dives is given in Table IX. DISCUSSION This project was originally intended to see what type of decompression schedule profiles would develop if a model different from the classical model was considered. No attempt was or is made to correlate the ranks with anatomical sites. Depth/Time / / / / / / 7/ 7/ 7/ / / / 9/ 9/ 9/ / / /9 / / / /9 / / /9 / / /9 / / /9 / / /9 Non / / /9 Non.e available.e available TABLE VII U. S. Navy Diving Tables. Total Time.... 9.... 7..7 9. 9 7 7.... 9.7 9. 9...7.7.... 9. 9.. 7.... 7....... 7 7.7. 7. 9 9.....7. 7.. 7....7.. 9......
TABLE VIII Comparison of Analog Schedule with Hills' Titration of Foot Stop of Same / Dive. Stop TOTAL Analog Hills U. S. Navy (9) 9 * 9 9 9 7 *The analog was calibrated with foot stop as a safety factor. minutes at the Figure appears more complicated than it is. In it, the actual time for % and 9% saturation was measured. Then, assuming a simple exponential function, apparent times were calculated. If the saturation followed a simple exponential, the apparent values would fall on top of the measured values. Since they did not, it is shown that the apparent half-time is constantly changing with saturation. Clearly shown is that the halftime lengthens for the first four ranks, and shortens for the last three ranks. It does not change for the fifth rank. TABLE IX T. 9 No-Decompression Dives. Depth 7 9 Limit Ascent Rate unlimited / /, / /, / /, / /, / 9 /, / 9 /, /, / 7 /, /, / /, /, / /, /, / /, /, / /, /, / /, /, / /, /, / Rank Number If anyone desires to build such an analog for his own evaluation, it is fair to warn him that changing the time scale will change the ratios developed. Initially, the machine was calibrated to a six hour saturation period. With that, the pertinent ratio was.: instead of.:. However, the schedules produced for short dives were approximately the same. Notice in Figure the delay before the last ranks begin to saturate. In the time scale used, this means a delay of some - minutes before the last three ranks even begin to saturate. In the / dive, the last rank reached a peak of feet about minutes of decompression at the foot stop. Thus, the last ranks frequently continue to saturate well into the decompression. Figure -Measured Times of % and 9% Saturation. Also shown is apparent values if a simple exponential function is assumed and value is calculated from the other measured value. In Table II, it is clearly shown that the last two ranks play an important role in the overall behavior of the analog. They behave as a dam beyond which the electrons cannot go, and therefore determine what the final voltage will be when the excess electrons in the foremost ranks leak out into the last ranks. If there are too few ranks, the average voltage levels high... and decompression is needlessly prolonged; too many, and shallow stops are made too short for a short dive, too long for a saturation dive. 7
O o / / E * CLASSICAL HALDANE MODEL USING,,,,, ANALOG MODEL TIME SCALES ADJUSTED TO SIMULTANEOUS 9% SATURATION 7 so Hours Figure -Left is Classical Haldane Model using,,,,,. Right is Analog Model, Time Scales Adjusted to Simultaneous 9% Saturation. The present analog has too few ranks to be considered for a saturation dive. Figure is presented to help any investigator trying to decide how many ranks to use in an expanded version. If the trend for the first eight ranks holds up, it can be expected that an analog using the same size resistors and capacitors with fourteen ranks would have a maximum half-time of seconds. This is equivalent to minutes with the present time scale. Also, doubling the resistor size will double the half-time, and vice versa. Notice that the surfacing ratios from the foot stop in Table III are much lower than the ones from the and foot stops. When simulating this dive on the analog, it was noticed that the dive called for leaving the foot stop at minutes, while the voltages on the analog required an additional minutes at the foot stop. The voltage on rank peaked at. feet, twelve minutes into the foot stop, and remained there until minutes into the stop, at which time it began to drop. Thus, eighteen minutes of the foot stop are taken up for reversing the direction of flow, in spite of an foot negative pressure gradient. 9 I 7 9 7 a 9 Total Number Of Ranks Figure -Longest Half-Time in to Number of Ranks. LI Seconds Relative The lower ratios at feet support B. A. Hills' contention that bubble phenomena exist at feet. It does not support his argument that they exist at feet, since the bubbles could have been formed by an abbreviated foot stop. Indeed, the analog indicates that the standard foot stop is too short by about minutes. This may explain why some of his goats bent on the standard table. From Figure, it is evident that the interdependent analog reaches % saturation later than the classical Haldane model. However, it reaches % saturation sooner. This works to the diver's benefit on short dives, but to his detriment on longer dives. The most interesting finding is shown in Figure, where Behnke's empirical curve of nitrogen washout in man is superimposed on a summation of each rank's saturation. It is obvious that the fit is nearly perfect, and just as obvious that the classical model will not simulate this curve. The diving tables predicted by the analog are very interesting, but appear to be unduly short. However, when compared with Hills' data, the analog predicted schedule comes out two minutes longer than his careful titration.
I. 9 7 j. I 7 9 Minutes Figure -Desaturation of Rank #. And, if your attention is called to the /9 and / schedules which have similar decompression times in the U. S. Navy Standard Tables, you will see that the analog schedules are right in line. The analog schedules almost invariably have deeper stops, especially on longer dives. Certain dives, namely /9 and /9, developed a "saturation pattern" which would make them much too short if human saturation occurs in much over hours. Hesitation should be employed before using these two tables until a larger analog is tested. This pattern exists when the foot stop is around minutes and/or the foot stop is for about minutes, signifying that the last rank is controlling, and that there is no way to know if an additional rank would or would not control, if present. Another rank would mean longer stops than indicated by the present model. This is what is meant by the previous statement concerning the importance of the last two ranks: their' placement is just as critical as the choice of a dam site on a river, insofar as the diver is concerned. The "No-Decompression" dives given in Table XI are very significant, since at the lower depths the analog has predicted precisely what is in the U. S. Navy Tables. The classical method does not predict these dives, and the tables were empirically derived, at least for the shallower depths. The deeper dives calculated by the analog are shorter than the Navy Tables because a longer dive would necessitate a stop at feet under the criteria selected. The question arises, considering saturation diving, whether the analog would behave any differently than the classical exponential model, since the analog would obviously be controlled by the last rank. Figures and 7 were obtained by saturating all ranks and then allowing them to discharge to zero. It is evident from Figure 7 that the last rank does desaturate by a simple exponential function. However, there is a delay in the analog of some. minutes before this desaturation begins. If the "tissue" under consideration for a saturation dive were minutes half-time, would be equivalent to an extra wait of minutes at the first stop before any desaturation would occur in the last rank. After that, a simple exponential function would apply just as in the classical model. I I Minutes Figure 7-Semi-Log Plot of Figure. of. minutes at onset. Notice delay 9
With testing in practical applications there will come the inevitable modifications. Most obvious, of course, are the number of ranks and the ratios used. Although the present data would make it appear unnecessary, a hybrid model combining ideas of perfusion and diffusion could be easily constructed with separate diffusion analogs for each half-time "tissue." This is far beyond the scope or intent of the present paper. An inexpensive and easily constructed electric analog has been described. It is firmly felt that further investigation using this as a tool in studying decompression illness and in designing decompression schedules is warranted and required. REFERENCES. Behnke, A. R. Capt., MC, USN (Ret). The absorption and elimination of gases of the body in relation to its fat and water content. Med. (), 9.. Behnke, A. R., and T. L. Willmon. Gaseous nitrogen and helium elimination from the body during rest and exercise. Am. J. Phys. ():9-, 9.. Boycott, A. E., G. C. C. C. Damant, and J. S. Haldane. The prevention of compressed air illness. J. Hyg. :-, 9.. Hills, B. A. Relevant phase conditions for predicting occurrence of decompression sickness. J. Appl. Phys. ():-, 9.. Hills, B. A. A thermal analogue for the optimal decompression of divers. Phys. Med. Biol. : 7-, 97.. U. S. Navy., Diving Manual-Bureau of Ships. Washington, D. C.: U. S. Government Printing Office, 9.
UNCLASSIFIED DOCUMENT CONTROL DATA - R & D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) NAVAL SUBMARINE MEDICAL CENTER, Submarine Unclassified Medical Research LaboratorybGRU. REPORT TITLE DECOMPRESSION PATTERNS DEVELOPED BY AN INTERDEPENDENT ELECTRIC ANALOG. DESCRIPTIVE NOTES (Type Of report and inclusive dates) Report on in-house project S. AU THOR(S) (First name, middle initial, last name) Gary P. TODD, LT, MC, USNR. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS May 99 Sa. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) SMRL Report Number b. PROJECT NO. MR.-9. C. 9b. OTHER REPORT NO(S) (Any other numbers that may be assigned this report) d. O. DISTRIBUTION STATEMENT This document has been approved for public release and sale; its distribution is unlimited.. SUPPLEMENTARY NOTES. SPONSORING MILITARY ACTIVITY Naval Submarine Medical Center Box Naval Submarine Base Groton, Connecticut. ABSTRACT A simple, inexpensive electronic analog has been developed and constructed which is based on a modification to the classical Haldane mathematical model. Unlike the Haldane model this analog uses a series alignment of theoretical half-time tissues rather than the usual parallel arrangement. Schedules produced by this analog closely follow the experimental inert gas elimination curves developed by Behnke and the mathematical model theorized by B. A. Hills. The results raise an interesting question as to the adequacy of the present haldane model modification employed by the U.S. Navy for decompression schedule calculation. Further testing must be done before this latter question can be answered. DD 7R NOV7 (PAGE I) S/N -7- UNCLASSIFIED Security Classification ND PPSO
UNCLASSIFIED Security Classification.KEY WORDS LINK A LINK B LINK C ROLE WT ROLE WT ROLE WT Decompression schedules for divers Electronic decompression analog L DD,)ov, (PAGE ) DD ORM7 (BACK) I - A - & - I - A - A - UNCLASSIFIED Security Classification